Worked solution · Exam FM
This Exam FM sample reference tests Annuities. At time 5 the payments are 1,000 through 3,000, which decompose into a 500 level annuity-due plus 500 times an increasing annuity-due. Discounting that time-5 value by v to the fifth gives the expression in choice D.
Independent solution
Setup
Use time 5, the date of the first payment, as the local valuation date.
Model
Both local streams begin immediately at time 5, so they are annuities-due.
Compute
Bring the local value back five years to time 0.
Answer
This formula is exactly the expression in choice D.
Test the method on unseen problems
30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.
Original practice · fully worked
A five-payment grant begins with 600 at year 3, and each later annual payment is 200 larger. At a 5% annual effective yield, calculate the present value at time 0.
Discounting the five payments 600 through 1,400 from years 3 through 7 gives present value 3,850.40, choice B.
Setup
Generate the five payment amounts and their dates.
Model
Discount every payment directly to time 0 at 5%.
Compute
The five-term discounted sum is 3850.403044.
Answer
The grant's present value is 3,850.40, selecting choice B.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 113 Exam FM annuities and non-contingent cash flows practice problems.
Drill the method: Exam FM Annuities and Perpetuities problems
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